Nepal's King Gyanendra has called on opposition parties to put forward their candidate for prime minister, after weeks of protest against him.
In a televised address, he said he would return power to the people, but gave no date for elections to be held.
The offer came on the 16th day of protests against his direct rule.
King Gyanendra sacked the government and assumed direct powers in February 2005, ostensibly to quell long-running insurgency by Maoist rebels.
The BBC's Nick Bryant in Kathmandu says the king's move meets a major demand set by his opponents but the question is whether the people accept the concession.
He says initial reaction to the announcement was positive with cheering among the crowds, who think they have won a major victory.
Earlier, US ambassador James Moriarty warned the king could be forced from power within days unless he compromised.
Tens of thousands of people were back on the streets in Nepal's capital for a second day of mass protests on Friday, despite a shoot-on-sight curfew.
The renewed curfew began at 0900 (0315 GMT). It was due to be lifted at 2000 (1415 GMT), but has been extended for a further four hours, the Associated Press reported.
The demonstrations turned violent on Thursday in one area of Kathmandu, where police killed three people.
Mass demonstrations against King Gyanendra's absolute rule or against the monarchy itself have been going on for more than two weeks.
Eyewitnesses said the police had opened fire indiscriminately during Thursday's protests and that in addition to those who died, many had been seriously injured.
Another person died on Friday in the town Gulariya, some 500km (300 miles) south-west of Kathmandu, after being injured in protests a day earlier, reports say.
At least 14 demonstrators have now died around the country in the last two weeks.